# Sample Problem

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**Sample Problem**

Two metal spheres, suspended by vertical cords, initially just touch, as shown in . Sphere with mass m, = 30 g, is pulled to the left to height hI· = 8.0 em, and then released from rest. After swinging down, it undergoes an elastic collision with sphere 2, whose mass 2 = 75 g. What is the velocity just after the collision?

SOLUTION: A first Key Idea is that we can split this complicated motion into two steps that we can separately analyze: (I) the descent of sphere 1 and (2) the two-sphere collision.

Step 1. The Key ldea here is that as sphere I swings down, the . mechanical energy of the sphere- Earth system is conserved.

Step 2. Here we can make two assumptions in addition to the assumption that the collision is elastic. First, we can assume that the collision is one-dimensional because the motions of the spheres are approximately horizontal.

The minus sign tells us that sphere I moves to the left just after the collision.